Construction of New Class of Linear Multivariate Public Key Cryptosystem: Along With A Note on the Number 9999990 and its Application

摘要

多変数公開鍵暗号について新しいクラス，K(I)SE(1)PKC,を提案している．K(I)SE(1)PKCは線形多変数暗号という著しい特徴を有するが，確率的構造を有することにより線形攻撃に対し，十分な安全性を確保することが可能である．付録において，数9999990に関する考察を与えるとともに，この数に基づく素数高速生成への一応用を示す．%In this paper, we present a new class of linear multivariate PKC referred to as K(I)SE(1)PKC. We shall show that K(I)SE(1)PKC, a linear multivariate PKC, can be sufficiently secure against any linear transformation attack due to the probabilistic structure. We show that the probabilistic structure can be successfully introduced by the using of the Chinese Remainder Theorem. In Appendix, we shall discuss on the number 9999990. We shall show a simple application of this number when generating prime numbers, by taking advantage of the fact that it has all the prime numbers less than or equal to 13 as factors, i.e. 9999990 = 2×3×5×7×11×13×37.